Valence bond theoretical study for chemical reactivity

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Relativistic bond lengthening of UO 2 2+ and UO2

Summary Relativistic calculations on UO₂ [1] have shown that relativity leads to substantial bondlengthening in this compound, in contrast to the bond contraction found almost exclusively for other compounds. The bond lengthening isnot caused by the relativistic expansion of the 5f valence AO of U, which is the primary bond forming orbital on U in UO₂. The origin of the bond lengthening can be traced back to the semi-core resp. subvalence character of the U 6p AO. The valence character of 6p shows up in an increasing depopulation of the 6p upon bond shortening, and hence loss of mass-velocity stabilization. The core character of 6p shows up in large off-diagonal mass-velocity matrix elements 5p|h _MV|6p which are shown to have an overall bond lengthening effect. The larger expansion in UO₂ than in UO ₂ ²⁺ is due to destabilization of U levels in UO₂, caused by repulsion of the two additional 5f electrons.The present analysis corroborates the picture of relativistic bond length effects of Ref. [2].     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

Structural features of tricarbonyl(N-methyl-2-pyridinecarboxyamide)chloro-rhenium(I)-potential precursor of radiopharmaceuticals

Structural characteristics of the novel [fac-Re(CO)₃L]Cl complex, where L denotes the N-methyl-2-pyridinecarboxyamide, are presented. Molecular structure of the complex has been established by means of X-ray single crystal diffraction and compared with quantum mechanical calculations. It has been shown that pyridinethioamide is softer base than pyridineamide. As a result of different Re^I–S and Re^I–O bond covalent shortenings (reflecting their diverse ionic/covalent character ratio) difference of the bond lengths decreases from a theoretical value of 0.45 Å to the value of 0.28 Å.     

1,2-CF bond activation of perfluoroarenes and alkylidene isomers of titanium. DFT analysis of the C-F bond activation pathway and rotation of the titanium alkylidene moiety

Isomeric alkylidene complexes syn- and anti-(PNP)Ti[C^tBu(C₆F₅)](F) (1) and (PNP)Ti[C^tBu(C₇F₇)](F) (2) have been generated from C-F bond addition of hexafluorobenzene (C₆F₆) and octafluorotoluene (C₇F₈) across the alkylidyne ligand of transient (PNP)Ti≡C^tBu (A) (PNP⁻N[2-P(CHMe₂)₂-4-methylphenyl]₂), which was generated from the precursor (PNP)TiCH^tBu(CH₂^tBu). Two mechanistic scenarios for the activation of the C-F bond by A are considered: 1,2-CF addition and [2 + 2]-cycloaddition/β-fluoride elimination. Upon formation of the alkylidenes 1 and 2, the kinetic and thermodynamic alkylidene product is the syn isomer, which gradually isomerizes to the corresponding anti isomer to ultimately establish an equilibrium mixture (when using 1, 65/35) if the solution is heated in benzene to 105 °C for 1 h. Single crystal X-Ray crystallographic data obtained for the two isomers of 2 (and syn isomer of 1) are in good agreement with computed DFT-optimized models. Our calculations suggest convincingly that the isomerization process proceeds via a concerted rotation involving a heterolytic bond cleavage about the alkylidene bond. The two rotamers are thermodynamically very close in energy and interconvert with an estimated barrier of ∼26 kcal/mol. The electronic reason for this unexpectedly low barrier is investigated.     

Push-pull alkenes from cyclic ketene-N,N′-acetals: a wide span of double bond lengths and twist angles

Push-pull alkenes can be quickly accessed by cyclic ketene-N,N′-acetal chemistry. A number of push-pull structures with a wide span of double bond lengths and twist angles were synthesized from the reactions of (1) N,N′-dimethyl cyclic ketene-N,N′-acetals with isocyanates, (2) the products from (1) with isocyanates, (3) 2-methylimidazoline and 2-methyl-1,4,5,6-tetrahydropyrimidine with diacid chlorides, (4) 2-methylimidazoline, and 1,2-dimethyl-1,4,5,6-tetrahydropyrimidine with benzoyl chlorides, and (5) 1,2-dimethylimidazoline and 1,2-dimethyl-1,4,5,6-tetrahydropyrimidine with aryl isocyanates. These reactions proceed under very mild conditions and give moderate to excellent yields. X-ray crystallographic analysis of eight pxush-pull alkenes indicates that the central double bond lengths and twists are sensitive to the ring sizes (5 or 6), ring structures (fused or non-fused), electron donating and withdrawing strengths of pushing and pulling portions, respectively, number of electron pushing or pulling groups and substituent steric effects.     

A valence bond study of the oxygen molecule

Ab initio valence bond calculations are performed for the three lowest states of the oxygen molecule (³Σ⁻_g, ¹Δ_g, and ¹Σ⁺_g). One objective of the present study was to make a contribution to previous valence bond discussions about the oxygen “double” bond. Further, we study the origin of a small barrier in the potential energy surface of the ground state. Two compact models are employed to maintain the clear picture that can be offered by the valence bond method. The first model has only the Rumer structures that are essential for bonding and a proper dissociation. The second model, in addition, has structures which represent excited atoms. These prove to be important for the dissociation energies. For both models, the orbitals are fully optimized. The spectroscopic data obtained are significantly better than are the (few) valence bond results on O₂ that have been published and have the quality of multiconfiguration self-consistent field calculations in which the same valence space is used. The “hump” in the potential energy surface of the ground state is shown to arise from a spin recoupling. The free atoms correspond to a spin coupling that is incapable of describing the formation of bonds. Only at short distances, an alternative spin coupling provides bonding and the repulsive curve is converted into an attractive one. Our results on this subject support a valence bond explanation previously given by McWeeny [R. McWeeny, Int. J. Quantum Chem. Symp. 24 , 733 (1990)]. © 1996 John Wiley & Sons, Inc.     

Ionization,atomization, and bond energies as functions of distances in inorganic molecules and crystals

The ionization potentials and dissociation energies of diatomic molecules are determined as functions of bond length, and the atomization energies of metals and crystalline compounds are determined as E = a/d ⁿ functions. In most cases, n ≥ 1; but for a number of metals and compounds, n < 1, as distinct from all known types of interatomic interactions. It is shown that the ratios of the bond energies and bond lengths of Group 1A and 1B metals to the respective molecular parameters have similar values, proving the identical valence states of the atoms of these metals in crystal structures.     

Crystallographic studies and physicochemical properties of π-electron systems: Part VIII. Crystal and molecular structure of N,N-dimethyl-4-nitro-2, 6-xylidine. Application of the Walsh Rule to p-substituted nitrobenzenes

The crystal and molecular structure of N,N-dimethyl-4-nitro-2, 6-xylidine has been determined by X-ray diffraction. The compound crystallizes as tetragonal bipyramids, space group P4₁2₁2 with cell dimensions a=764.1(1), c=1807.9(2) pm. The absolute configuration was not determined. The structure was solved by direct methods and refined to R=0.042 for 578 observed reflections. The e.s.d. values of bond lengths between the heavy atoms are 0.3–0.4 pm and of the valence angles are 0.1–0.3°. The NO₂-plane is coplanar with e.s.d. 0.21° with the plane of the benzene ring, whereas the NMe₂-plane is twisted by 60.40(30)° outwards. The through resonance is hence hindered and in turn, the geometry of the ring exhibits less quinoidal character. These deformations are analyzed in terms of the Walsh rule applying parameters determined directly from bond lengths, as well as applying the HOSE-model. Comparison with 14 well solved structures for which the e.s.d. values for bond lengths are not higher than 0.5 pm of p-substituted nitrobenzenes, leads to the conclusion that consideration of the difference in length for bonds C2C3 and C1C2 describes the substituent effect on the geometry of the ring almost as well as the valence angle α at C1.     

Estimation of the 2.05 helix type i→i hydrogen bond energy at Aib-Oxa motif: an isodesmic approach

Bending at the valence angle N–C^α–C′ (τ) is a known control feature for attenuating the stability of the rare intramolecular i→i hydrogen bonded pseudo five-membered ring C₅ structures, the so called 2.0₅ helices, at Aib. The competitive 3₁₀-helical structures still predominate over the C₅ structures at Aib for most values of τ. However at Aib^∗, a mimic of Aib where the carbonyl O of Aib is replaced with an imidate N (in 5,6-dihydro-4H-1,3-oxazine = Oxa), in the peptidomimic Piv-Pro-Aib^∗-Oxa (1), the C₅i structure is persistent in both crystals and in solution. Here we show that the i→i hydrogen bond energy is a more determinant control for the relative stability of the C₅ structure and estimate its value to be 18.5 ± 0.7 kJ/mol at Aib^∗ in 1, through the computational isodesmic reaction approach, using two independent sets of theoretical isodesmic reactions.     

Classical structures in modern valence bond theory

The results of some recent ab initio valence bond calculations, in which both structure coefficients and orbital forms are optimized, are analysed. The origin of structures in which the optimum orbitals are no longer atomic in character but instead delocalized, is traced back to the presence of certain symmetries in the wavefunction. When such symmetries exist it is possible to choose alternative linear combinations of the delocalized orbitals and to rewrite the wavefunction in terms of VB structures of classical form. The advantages of the classical structures are discussed in the context of a simple example — a square planar conformation of four hydrogen atoms.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Bond dissociation energies and bond orders for diatomic alkali halides

The bond dissociation energies for Alkali halides have been estimated based on the derived relations: $$\begin{gathered} D_{AB} = \bar D_{AB} + 31.973{\text{ e}}^{0.363\Delta x} {\text{ and}} \hfill \\ D_{AB} = \bar D_{AB} (1 - 0.2075\Delta xr_e ) + 52.29\Delta x, \hfill \\ \end{gathered} $$ where \(\bar D_{AB} = (D_{AA} \cdot D_{BB} )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) , Δx represents Pauling electronegativity differences x(_A ?x_B) and r _e is the internuclear distance. A simplified formula relating bond orders, q, to spectroscopic constants is suggested. The formula has the form q = 1.5783 × 10^?3 (ω _e ² r_e/ B_e)^1/2. The ambiguity arising from the Parr and Borkman relation is discussed. The present study supports the view of Politzer that q/(0.5r _e)² is the correct definition of bond order. The estimated bond energies and bond orders are in reasonably good agreement with the literature values. The bond energies estimated with the relations we suggested, for alkali halides give an error of 4.5% and 5.3%, respectively. The corresponding error associated with Pauling's equation is 40.2%.     

Hydrogen bonding and halogen bonding co-existing in the reaction of heptafluorobenzyl iodide with N,N,N,N-tetramethylethylene diamine

Two novel assembling systems 3 and 4, with the structures of C₆F₅CF₂⁻?H⁺N(Me)₂CH₂CH₂(Me₂)N⁺H?⁻CF₂C₆F₅ and C₆F₅CF₂I?N(Me)₂CH₂CH₂(Me)₂N?ICF₂C₆F₅, respectively, have been generated from the solution of heptafluorobenzyl iodide 1 and N,N,N^′,N^′-tetramethylethylenediamine 2 in dichloromethane. Their structures have been characterized by X-ray diffraction analysis, NMR and IR spectroscopy. Intermolecular N?I halogen bond and F?H hydrogen bond are revealed to be the driving forces for their formation.     

Electrostatic MO-O (methanol) bond in benzyltriphenylphosphonium trans-tetrachloro(methanol)oxomolybdate(V)

Benzyltriphenylphosphonium trans-tetrachloro(methanol)oxomolybdate(V) has been obtained from methanol suspension of benzyltriphenylphosphonium molybdate(VI) saturated with hydrogen chloride. The crystal structure comprises discrete trans-tetrachloro(methanol)oxomolybdate(V) anions and benzyltriphenylphosphonium cations. The anion has distorted octahedral geometry of central atom with visible trans influence imposed by short Mo-O bond (1.659(2) Å). The methanol O atom is bonded to the Mo atom, the bond being mostly electrostatic in character. A comparison with previously reported structures indicates that the methanol methyl moiety can switch between different positions with respect to the chloride ligands.